%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : SWX207+1 : TPTP v9.3.1. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n002.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 01:45:34 PM UTC 2026
% Result : Theorem 1.00s 0.48s
% Output : Proof 1.00s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWX207+1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.21 % Computer : n002.cluster.edu
% 0.07/0.21 % Model : x86_64 x86_64
% 0.07/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.21 % Memory : 8046.5625MB
% 0.07/0.21 % OS : Linux 6.8.0-71-generic
% 0.07/0.21 % CPULimit : 300
% 0.07/0.21 % WCLimit : 300
% 0.07/0.21 % DateTime : Mon Sep 28 15:11:13 UTC 2026
% 0.07/0.21 % CPUTime :
% 0.07/0.21 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.00/0.48 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --complete-subsets --ground-joining-incomplete-limit 15 --flatten-every 2
% 1.00/0.48
% 1.00/0.48 % SZS status Theorem
% 1.00/0.48
% 1.00/0.49 % SZS output start Proof
% 1.00/0.49 Axiom 1 (axiom_025): linP(pE) = nil.
% 1.00/0.49 Axiom 2 (axiom_023): linP(pA) = cons(a, nil).
% 1.00/0.49 Axiom 3 (axiom_019): append(nil, X) = X.
% 1.00/0.49 Axiom 4 (axiom_026): linC(c2(X, Y)) = append(linP(X), linP(Y)).
% 1.00/0.49 Axiom 5 (axiom_017): proj1C(c2(X, Y)) = X.
% 1.00/0.49 Axiom 6 (axiom_020): append(cons(X, Y), Z) = cons(X, append(Y, Z)).
% 1.00/0.49 Axiom 7 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 1.00/0.49 Axiom 8 (goal_027): ifeq(linC(X), linC(Y), X, Y) = Y.
% 1.00/0.49 Axiom 9 (axiom_021): linP(aP(X)) = append(cons(a, nil), append(linP(X), cons(a, nil))).
% 1.00/0.49
% 1.00/0.49 Lemma 10: cons(a, append(linP(X), linP(pA))) = linP(aP(X)).
% 1.00/0.49 Proof:
% 1.00/0.49 cons(a, append(linP(X), linP(pA)))
% 1.00/0.49 = { by axiom 2 (axiom_023) }
% 1.00/0.49 cons(a, append(linP(X), cons(a, nil)))
% 1.00/0.49 = { by axiom 3 (axiom_019) R->L }
% 1.00/0.49 cons(a, append(nil, append(linP(X), cons(a, nil))))
% 1.00/0.49 = { by axiom 6 (axiom_020) R->L }
% 1.00/0.49 append(cons(a, nil), append(linP(X), cons(a, nil)))
% 1.00/0.49 = { by axiom 9 (axiom_021) R->L }
% 1.00/0.49 linP(aP(X))
% 1.00/0.49
% 1.00/0.49 Goal 1 (axiom_010): aP(X) = pE.
% 1.00/0.49 The goal is true when:
% 1.00/0.49 X = pE
% 1.00/0.49
% 1.00/0.49 Proof:
% 1.00/0.49 aP(pE)
% 1.00/0.49 = { by axiom 5 (axiom_017) R->L }
% 1.00/0.49 proj1C(c2(aP(pE), pA))
% 1.00/0.49 = { by axiom 8 (goal_027) R->L }
% 1.00/0.49 proj1C(ifeq(linC(c2(pE, aP(pA))), linC(c2(aP(pE), pA)), c2(pE, aP(pA)), c2(aP(pE), pA)))
% 1.00/0.49 = { by axiom 4 (axiom_026) }
% 1.00/0.49 proj1C(ifeq(append(linP(pE), linP(aP(pA))), linC(c2(aP(pE), pA)), c2(pE, aP(pA)), c2(aP(pE), pA)))
% 1.00/0.49 = { by axiom 4 (axiom_026) }
% 1.00/0.49 proj1C(ifeq(append(linP(pE), linP(aP(pA))), append(linP(aP(pE)), linP(pA)), c2(pE, aP(pA)), c2(aP(pE), pA)))
% 1.00/0.49 = { by axiom 1 (axiom_025) }
% 1.00/0.49 proj1C(ifeq(append(nil, linP(aP(pA))), append(linP(aP(pE)), linP(pA)), c2(pE, aP(pA)), c2(aP(pE), pA)))
% 1.00/0.49 = { by axiom 3 (axiom_019) }
% 1.00/0.49 proj1C(ifeq(linP(aP(pA)), append(linP(aP(pE)), linP(pA)), c2(pE, aP(pA)), c2(aP(pE), pA)))
% 1.00/0.50 = { by lemma 10 R->L }
% 1.00/0.50 proj1C(ifeq(linP(aP(pA)), append(cons(a, append(linP(pE), linP(pA))), linP(pA)), c2(pE, aP(pA)), c2(aP(pE), pA)))
% 1.00/0.50 = { by axiom 1 (axiom_025) }
% 1.00/0.50 proj1C(ifeq(linP(aP(pA)), append(cons(a, append(nil, linP(pA))), linP(pA)), c2(pE, aP(pA)), c2(aP(pE), pA)))
% 1.00/0.50 = { by axiom 3 (axiom_019) }
% 1.00/0.50 proj1C(ifeq(linP(aP(pA)), append(cons(a, linP(pA)), linP(pA)), c2(pE, aP(pA)), c2(aP(pE), pA)))
% 1.00/0.50 = { by axiom 6 (axiom_020) }
% 1.00/0.50 proj1C(ifeq(linP(aP(pA)), cons(a, append(linP(pA), linP(pA))), c2(pE, aP(pA)), c2(aP(pE), pA)))
% 1.00/0.50 = { by lemma 10 }
% 1.00/0.50 proj1C(ifeq(linP(aP(pA)), linP(aP(pA)), c2(pE, aP(pA)), c2(aP(pE), pA)))
% 1.00/0.50 = { by axiom 7 (ifeq_axiom) }
% 1.00/0.50 proj1C(c2(pE, aP(pA)))
% 1.00/0.50 = { by axiom 5 (axiom_017) }
% 1.00/0.50 pE
% 1.00/0.50 % SZS output end Proof
% 1.00/0.50
% 1.00/0.50 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------